منابع مشابه
Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background
Several recent approaches to black hole entropy obtain the density of states from the central charge of a Liouville theory. If Liouville theory is coupled to a dynamical spacetime background, however, the classical central charge vanishes. I show that the central charge can be restored by introducing appropriate constraints, which may be interpreted as fall-off conditions at a boundary such as ...
متن کاملLiouville numbers
In this work, we define the concept of Liouville numbers as well as the standard construction to obtain Liouville numbers and we prove their most important properties: irrationality and transcendence. This is historically interesting since Liouville numbers constructed in the standard way where the first numbers that were proven to be transcendental. The proof is very elementary and requires on...
متن کاملChiral Liouville Gravity
Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the r...
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Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.
متن کاملSturm-liouville Eigenvalue Characterizations
We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2020
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2019.108351